Improving financial conditions of ATEs in the city of Dnipro basing upon optimal assignment of vehicle fleet to the routes

ICCPT 2019: Current Problems of Transport: Proceedings of the 1st International Scientific Conference, May 28-29, 2019, Ternopil, Ukraine

ICCPT 2019: Current Problems of Transport. https://iccpt.tntu.edu.ua

© 2019 The Authors. Published by TNTU Publ. and Scientific Publishing House “SciView”.

Improving financial conditions of ATEs in the city of

Dnipro basing upon optimal assignment of vehicle

fleet to the routes

Igor Taran, Vadim Litvin

National Technical University “Dnipro Polytechnic”, 19 D. Yavornytsky Ave., Dnipro, 49005, Ukraine, taran7077@gmail.com

Abstract: Topicality of the problem solution concerning optimal assignment of vehicles to municipal

routes for auto-transport enterprises (ATE) in the city of Dnipro has been substantiated. Technological and economic evaluation of DATP 11255 PJSC activity has been represented. An overview of the available models to assign buses to routes with the determination of their sphere of use has been given; key advantages and disadvantages have been specified. Structure of the model for optimal assignment of buses to the routes have been proposed where target function is represented by maximization of ATE income, and the restriction is represented by non-exceedance of maximum admissible values of traffic interval and coefficients of bus capacity use. Passenger flow in terms of DATP 11255 PJSC routes during morning rush hour has been studied by means of table method. Basic technical-operational and economic parameters of the operation of DATP 11255 PJSC routes have been evaluated. Microsoft Excel SOLVER add-in has been applied to obtain optimal assignment of bus departures which will make it possible to do the following: to increase DATP 11255 PJSC income by 2.62 times (from 462.8 UAH/hour up to 1 211.8 UAH/hour); to improve quality of transportation process owing to the reduced maximum coefficient of the bus capacity use; and to ensure non-exceedance of maximum admissible bus traffic interval.

Keywords: target function, restriction system, optimal assignment, prime cost.

1. Introduction

Public municipal passenger transport (PMPT) is a complex multilevel system which studying requires using methods of system analysis; the methods include complex research of PMPT functioning problems and development of efficient tools for its improvement [1].

Optimal vehicle fleet assignment to the routes is one of the possible technological measures aimed at improvement of ATE condition and quality of passenger transportation in terms of municipal bus routes. That assignment should include the following: possibility to obtain the required output information (results of passenger flow studies), stochastic nature of the transportation process; necessity to optimize two interrelated parameters – number and capacity of the route buses; and the available technological and social restrictions.

However, it should be noted that while solving the problem of optimal assignment, certain difficulties occur stipulated by the problem multivariance; that multivariance prevents form the problem solution by simple enumeration of possibilities. Moreover, majority of the available methodologies takes into account parameters of the passenger service quality but not the financial situation of ATE. Thus, in terms of modern conditions, a problem of vehicles assignment to the routes should be solved involving optimization methods, and target function (or its restriction) should consider needs and possibilities of all the participants of a transportation process.

2. Literature review

Solution of the problem of optimal vehicles assignment to the routes means the provision of equal satisfaction of the passengers’ needs in term of their transportation on different routes taking into consideration a parameter of passenger service level, ATE costs, and technological restrictions (maximum traffic interval, bus stop capacity, number of buses etc.). In terms of its content, the problem belongs to the class of problems dealing with the production resources allocation aimed at reaching maximum efficient operation [3]. A method, in terms of which buses are assigned to the routes proportionally to the value of maximum passenger flows within the most loaded route section, is the most widely used one [4]. That method differs with its simplicity; however, it does not take into account quality of passenger service, effect of random factors, volumes and peculiarities of passenger flows within other (not so loaded) route sections, and structure of the fleet of vehicles being assigned.

Paper [5] represents different modifications of the assignment model [4] which propose to assign the routes proportionally to the volume of possible transport operation, proportionally to the transportation volumes, and proportionally to weighted average trip time. In term of the methods for bus assignment to the routes proposed in paper [6], bus traffic and passenger flow are analyzed with the consideration of random factors; probability of the fact that a passenger may not be allowed to board the bus on different routes is the criterion to assign buses. However, labour-consuming graphic constructions are required to obtain such solutions. That restricts the application of the methodology by the problems of research nature and complicates its use during short-time planning of transportation processes.

Thus, generalization of the analyzed assignment methodologies indicates that the models proposed in [4-6] are not optimization ones; correspondingly, the result, obtained with their help, is likely to be not optimal. However, main disadvantage of the majority of current assignment methodologies is in the fact that they were developed in 1970s-1990s before the changes in economic conditions on transport. Consequently, they do not take into consideration ATE interest in economic results of its activity.

3. Materials and methods

In recent years, numerous cities and towns in Ukraine have been demonstrating a tendency to the reduction in both volumes and quality of passenger transportation. That is the result of following factors: general economic crisis; reduced number of the vehicles due to their obsolete and technical depreciation; insufficient budgetary financing to cover losses due to the transportation of benefit-entitled passengers etc. All the mentioned factors result in unprofitability or low economic efficiency of the most Ukrainian ATEs.

the qualitative and substantiated (involving current methods of system analysis) solution of those problems.

Unfortunately, insignificant attention is currently paid to the solution of problem concerning optimal assignment of vehicles to the routes. First of all, that fact is explained by insufficient professional qualification of ATE employees who tends to solve their economic problem at the expense of passengers; secondly, there are no unified criteria which would take into consideration the needs of both transporters and passengers. Thus, development of innovative models and methodologies (which will take into account current conditions of ATE operation) and obtaining optimal (rational) variants for bus assignment to the routes are rather burning issues.

DATP 11255 PJSC has been selected as the basic enterprise for the study. Currently, the enterprise

services 6 municipal public routes. Passenger vehicle fleet includes 96 buses, 74% of which is accounted for Mercedes Sprinter and RUTA-22; the rest is accounted for BAZ А079, Bohdan А091, Bohdan А144, and Mercedes О345. Tables 1 and 2 represent assignment of buses to the routes and their basic characteristics respectively. Table 3 shows basic calculation categories for incomes and costs during the transportation process in 2018 (they were calculated on the basis of information represented in [9] as well as current route documents). Analysis of the data in Table 3 proves that nowadays DATP 11255 PJSC is the unprofitable enterprise (at least, according to the released reports). Total amount of losses in 2018 was UAH 2 657 442. According to the employees of the AME operations department, problem of the bus assignment to the routes was of empiric nature without the use of optimization economic and mathematical methods and consideration of the majority of technical and operational parameters of the transportation process.

While organizing the operation of passenger transport, complexity of the approach while selecting optimal solutions is stipulated by internal contradictions of the parameters of ATE efficient operation and quality of passenger service. That is why, this problem is most often reduced to the problem with a single parameter, determining one (basic) criterion; other parameters are with the imposed restrictions.

Table 1. Current assignment of buses to DATP 11255 PJSC routes. Bus model Passenger

capacity Route number Total #33 #76 #76А #79 #90 #156 Mercedes Sprinter 18 16 11 8 18 53 Ruta-22 22 8 10 18 BAZ А079 40 10 10 Bohdan А091 50 4 5 2 11 Bohdan А144 80 2 2 Mercedes О345 92 2 2 Total 12 28 10 18 10 18 96

Table 2. Basic characteristics of the routes.

Parameter Unit of measurement Route number #33 #76 #76А #79 #90 #156 Tariff UAH 7.0 7.0 7.0 7.0 10.0 7.0 Route length km 17.4 19.6 18.7 16.1 26.4 20.7

Trip time min 60 84 80 54 80 63 Operational speed km/hour 17.4 14.0 14.0 17.9 19.8 19.7

Table 3. Costs and incomes of DATP 11255 PJSC in 2018.

Route number #33 #76 #76А #79 #90 #156 Total

Wages, UAH 2 289 925 4 298 158 1 930 958 2 148 883 1 736 134 2 017 257 14 421 318 Social deductions, UAH 915 970 1 228 045 508 147 920 950 631 322 1 100 322 5 304 757 Fuel and lubricants, UAH 6 106 467 10 745 394 3 760 286 5 986 173 5 208 403 7 702 256 39 508 988 Tyres, UAH 610 647 2 149 079 406 517 613 966 1 736 134 916 935 6 433 280 Amortization, UAH 1 221 293 1 842 068 813 035 1 074 441 1 420 474 1 467 096 7 838 409 Maintenance and repair, UAH 2 442 587 6 754 248 1 626 070 2 762 849 2 998 778 2 384 032 18 968 566 Other costs, UAH 1 679 279 3 684 135 1 117 923 1 841 899 2 051 795 2 750 806 13 125 840

Sum of costs ,

UAH 15 266 168 30 701 126 10 162 934 15 349 162 15 783 040 18 338 704 105 601 158 Total run, km 1 090 441 1 918 820 671 480 1 068 960 930 072 1 375 403 7 055 175

Trip time, hour 62 669 137 059 47 877 59 756 46 973 71 849 426 183

Number of trips 62 669 97 899 35 908 66 395 35 230 68 428 366 529

Anticipated

income, UAH 16 875 323 31 953 326 12 756 845 16 566 482 16 693 314 25 027 515 119 872 806 Real income, UAH 14 681 531 30 355 659 9 950 339 14 578 504 15 357 849 18 019 811 102 943 694

Losses, UAH 584 637 345 467 212 595 770 658 425 191 318 893 2 657 441

Under conditions of complicated economic situation which is characteristic for the majority of ATEs (including the ones in Dnipro), optimality criterion should contain not only parameters of the service quality but also their economic efficiency. Taking into consideration all the aforementioned, the authors propose following structure for the model of optimal assignment of buses to the routes; in terms of the model, maximization of ATE income is the target function (depending upon the selected assignment variant), and restrictions are represented by non-exceedance of maximum admissible values of traffic interval and coefficients of bus capacity use:

                      





   0 . min 15 2 , 1 max 1 max max j 1 1 ij n j i ij j j і m i n j і ij A A A I I D q A





(1) (2) (3) (4) (5)

where Aij - is number of buses (taking into consideration specificity of obtaining input data at that

stage, not the number of buses but number of departures) of ith _{model on j}th _{route (assignment plan} being developed); qi - is capacity of ith bus model; Dij - is income of ATE from the operation of a

passenger unit of ith _{model on j}th _route;

j



- is coefficient of bus capacity use in terms of the most loaded trip of jth _route; max _{- is maximum admissible coefficient of bus capacity use (taking into}

account control of transportation process quality, it is proposed to take max_{=1.20 for all routes);}

j

I

- is bus traffic interval on jth _route; max

I - is maximum admissible bus traffic interval (taking into account control of transportation process quality, it is proposed to take max

i

A - is available number of buses of ith _model;

_m

_{- is number of bus models being assigned;}

_n

_{- is} number of routes being serviced.

Tables 1 and 2 represent basic parameters of the operation of DATP 11255 PJSC routes (operational velocity Vj , trip duration tj, bus capacity q , fare i Tj etc.) required to calculate

constituents of the proposed models (1-5). Table 3 contains data on the constituents of prime cost of the transportation process required to calculate variable v

j

C and constant costs Ccj for bus

operation.

As for the data concerning values of the coefficient of passenger variation



_j, dynamic coefficients of bus capacity use d

j



, maximum values of passenger flows max j

Н , and coefficients of capacity use in terms of the most loaded bus trip max

i

 , that information is possible to obtain only during the inspection of passenger flows.

Morning rush hour is the most important period for AME operation; thus, decision has been made to inspect passenger flows on all the routes of DATP 11255 PJSC from 8 a.m. to 9 a.m. (that is the period characterized by the greatest number of bus departures according to current bus schedules) only for direct route. To reduce labour consumption of the studies, recommendations from paper [10] were used as the substantiation of the sampling to guarantee sufficient accuracy of the obtained results. Basing upon recommendations [10] and current traffic interval, 21 bus trips are required to be studies in the context of the passenger flows inspection. Table 4 represents generalized information on the number of inspected trips, traffic intervals, and sampling percentage. Table 3 shows generalized results of the passenger flows inspection on DATP 11255 PJSC routes.

Basing upon the TEP data obtained during the inspection of passenger flows on DATP 11255 PJSC routes (Table 5), economic parameters of transportation process have been calculated which are required to obtain optimal bus assignment according to (1-5). Table 6 demonstrates the calculation results.

Problem of the vehicle fleet assignment to the municipal routes belongs to a special class of linear programming which are called transportation problems [1]. Special structure of a transportation problem helps apply following methods for its solution [11]: method of northwest angle, least-cost method, and Vogel’s approximation method. According to the recommendations proposed in paper [7,10], it is appropriate to use Microsoft Excel SOLVER add-in while solving problems of mathematical programming with economic (technical) focus; that is a powerful auxiliary tool to perform complicated calculations including solution of the majority of mathematical programming problems.

Table 4. Substantiation of minimal number of trips for the inspection.

Route number #33 #76 #76A #79 #90 #156

Class I

Number of departures 1 1 Traffic interval, min 60 60 Selectivity, % 100% 100% Number of inspections 1 1

Class А

Number of departures 2 4 3 1 Traffic interval, min 30 15 20 60 Selectivity, % 50% 50% 67% 100% Number of inspections 1 2 2 1

Class В

Table 5. Basic technical and operational parameters of the routes serviced by DATP 11255 PJSC during morning rush hour.

Parameter Route number

#33 #76 #76А #79 #90 #156

Number of the transported

passengers 292 560 222 440 122 258 Proposed passenger capacity 188 330 88 350 104 162 Maximum passenger flow 182 428 158 328 93 216 Dynamic coefficient of the

capacity use 0.63 0.88 1.21 0.63 0.72 0.86 Average duration

of one passenger trip 7.0 10.2 8.9 8.0 16.2 11.2 Coefficient of variation 2.49 1.92 2.10 2.01 1.63 1.85

Table 6. Economic parameters of the operation of DATP 11255 PJSC routes.

Parameter Bus model Route number

#33 #76 #76А #79 #90 #156 Tariff, UAH 7.00 7.00 7.00 7.00 10.00 7.00 Remuneration coefficient 0.91 0.93 0.91 0.92 0.90 0.89 Variablecosts, UAH/km 8.40 10.24 8.63 8.76 9.80 8.00 Constant costs, UAH/hour 97.44 80.64 91.28 100.18 83.16 105.14

Productivity, pas./seat 1.56 1.69 2.53 1.26 1.17 1.59 Income, UAH 9.92 11.03 16.14 8.12 10.53 9.91 Prime cost Mercedes Sprinter 13.53 17.42 15.73 12.84 20.53 15.33 Ruta-22 11.07 14.25 12.87 10.51 16.80 12.55 BAZ А079 6.09 7.84 7.08 5.78 9.24 6.90 Bohdan А091 4.87 6.27 5.66 4.62 7.39 5.52 Bohdan А144 3.05 3.92 3.54 2.89 4.62 3.45 Mercedes О345 2.65 3.41 3.08 2.51 4.02 3.00 Income Mercedes Sprinter -3.62 -6.39 0.42 -4.73 -10.00 -5.42 Ruta-22 -1.16 -3.22 3.27 -2.39 -6.27 -2.64 BAZ А079 3.83 3.19 9.07 2.34 1.29 3.01 Bohdan А091 5.04 4.76 10.48 3.49 3.14 4.39 Bohdan А144 6.87 7.11 12.60 5.23 5.91 6.46 Mercedes О345 7.27 7.62 13.07 5.61 6.51 6.91

Output data for SOLVER add-in should be represented in the form of electronic table containing four range types:

- range of the problem variables;

- range of the specified problem parameters; - range of the intermediate results;

- range of the target functions.

Range of the problem variables is the obligatory one; its configuration reminds a form of ATE fleet

matrix A being assigned. Each box of the range corresponds to one element Aij of matrix Awhich

corresponds to the number of bus departures of ith _{model operating on j}th _{route. Variable box should not}

contain any formulas.

Range of the specified problem parameters is the obligatory one containing constants preset by the

problem condition. In terms of the problem of bus assignment to the routes, that range has four constituent parts:

- sub-range for the vector assigning number of buses of ith _model

 

i

A

K  (at this stage, A_i

means number of departures of ith _{bus model within the time period being considered);}

- sub-range for the vector of maximum admissible value of the coefficient of bus capacity use on jth

routemax_{= [} max

j



]=1.2;

- sub-range for the vector of maximum admissible bus traffic interval on jth _route max

I = [ max

j

I ]=15

min.

Boxes of all the sub-ranges should not contain any formulas. All the output data should be entered

into those sub-ranges before the beginning of the problem solving.

Range of the intermediate results contains formulas representing dependences between the table

data being distributed within the three sub-ranges:

- sub-range of passenger-unit assignment to the routes Q=[Qij] for the products of matrix A

elements by corresponding elements of matrix q. Each box should contain a formula determining product A ij qi.

- sub-range of restriction functions of type (2) determining values of the coefficient of the vehicle fleet capacity use within the most loaded trip



j on jth route. That is a mandatory range; each of its

boxes contains following formula:



  _m i ij max j j Q H 1 max



.

- sub-range of the restricted-type functions (3) determining interval of bus trip Ij on jth route.

That is mandatory range; each of its boxes contains following formula:



  _m i ij j А I 1 60 .

- sub-range of the restriction function of type (4) determining number of buses of ith _{model being}

assigned on jth _{route. That is a mandatory range; each of its boxes contains formula}



 n j ij A 1 .

Range of the target function F should consist one (and only one) box with the formula to

determine criterion (1), i.e. formula of double sum

 

  m i n j іj F 1 1 .

To evaluate the efficiency of optimal vehicle fleet assignment to the routes, first of all, value of target function (1) in terms of the available organization of transportation process at DATP 11255 PJSC should be determined.

Owing to the fact that technical and operational parameters of the routes operation (Table 5) were obtained during the passenger flow inspection during morning rush hour (8 a.m. – 9 a.m.), current bus assignment to the routes should be understood not as the number of buses reserved for the routes (Table 1), but the number of their departures within the period being analyzed. Figure 1 shows data concerning the number of departures of ith _{bus model on j}th _{route. Those data are the range of problem}

variables. Each box of the range corresponds to one element Aij of matrix A.

To determine value of target function (1), it is required to calculate matrix of the proposed passenger-units Qij Aijqi and matrix of the target function constituents Fij DijQij. Results of

calculated Qij and Fij for current assignment are also represented in Fig.1. The obtained results

prove that the proposed capacity of buses on the routes are less that its demand (1 222<1 405), i.e. transportation process is performed in terms of deficit being 183 passenger-units. Income of DATP

11255 PJSC from 8 a.m. to 9 a.m. is UAH 462.8. Moreover, it should be noted that in terms of routes #76,

Figure 1. Work sheet of the prepared data for SOLVER add-in operation.

Optimal assignment of DATP 11255 PJSC buses was performed with the help of Microsoft Excel

SOLVER add-in. To perform the calculation, it is required:

- to call up SOLVER add-in: Service →Solver; - to indicate target box (J70) – functional (1);

- to indicate optimization direction – maximum value;

- to indicate variable boxes ($D$39:$I$44) – assignment planAij;

- to enter restrictions: ($D$59:$I$59<=$D$60:$I$60) – restriction (2); ($D$46:$I$46<=$D$47:$I$47) – (3); ($J$39:$J$44=$K$39:$K$44) – (4) and ($D$39:$I$44>=0) – restriction (5);

Figure 2 represents the results of Microsoft Excel SOLVER add-in. Thus, optimal assignment of DATP

11255 PJSC vehicles for morning rush hour has been obtained. Analysis of the information given in Figure 2

confirms that DATP 11255 PJSC income may be increased by 2.62 times (from UAH 462.8 up to UAH 1211.8). In addition, improvement of the transportation process quality should be emphasized as all the mentioned values of maximum coefficient of the buses capacity use are not more than admissible value



j<

max

Figure 2. Results of Microsoft Excel SOLVER add-in operation.

As previously stated, the obtained optimal distribution of buses to the routes (Figure 2) should be understood not as the number of buses reserved for the routes but as the number of their departures per period being analyzed. Thus, the obtained optimal plans of the departure assignments do not allow yet reserving all the vehicles of DATP 11255 PJSC for municipal routes being serviced.

At the moment, 96 buses (Table 1) are operated on the routes of DATP 11255 PJSC; assignment was performed for 43 vehicles (Table 1) as that is the amount of buses which is involved in transportation process for which TEP (Table 5) have been determined on the basis of passenger flows inspection.

Final reserving of DATP 11255 PJSC vehicle fleet for the municipal routes being serviced require additional assignment of 53 buses more (96–43=53) so that following condition will be met:

i n j final ij A A 



1 . (6)

Final number of buses of ith _{model which should operate on j}th _{route may be determined according}

where k is coefficient taking into account a degree of unassigned buses of i_i th _model:





    _n j ij n j ij i i A A A k 1 1 . (8)

Table 7 represents the results of calculation of the unassigned buses of ith _{model according to (8).} Table 6 shows the results of calculations of final reserving of DATP 11255 PJSC vehicle fleet for the routes (7).

Table 7. Calculation of the non-assignment degreek_i of ith _{model buses.}

Bus model



 n j ij A 1 i A



  n j ij i A A 1 i k Mercedes Sprinter 23 53 30 1.30 Ruta-22 8 18 10 1.26 BAZ А079 4 10 6 1.50 Bohdan А091 6 11 5 0.83 Bohdan А144 1 2 1 1.00 Mercedes О345 1 2 1 1.00 Total 43 96 53

Table 8. Final optimal assignment of buses to DATP 11255 PJSC routes

Bus model Passenger capacity Route number Total

#33 #76 #76А #79 #90 #156 Mercedes Sprinter 18 9 5 7 25 5 2 53 Ruta-22 22 5 5 8 18 BAZ А079 40 3 3 4 10 Bohdan А091 50 2 5 2 2 11 Bohdan А144 80 2 2 Mercedes О345 92 2 2 Total 16 14 12 30 10 14 96 4. Conclusions

Topicality of the solution of the problem concerning optimal vehicles assignment to the municipal routes in terms of ATEs of the city of Dnipro has been substantiated. The available models to assign buses to the routes has been analyzed with the specification of their area of application, basic advantages and disadvantages.

Structure of the model for optimal assignment of buses to the routes has been proposed; in terms of that structure, maximization of ATE income is a target function while restriction is represented by non-exceedance of maximum admissible values of traffic interval and coefficients of bus capacity use.

Microsoft Excel SOLVER add-in has been applied to obtain optimal assignment of buses departure

making it possible the following: to increase DATP 11255 PJSC income by 2.62 times (from UAH 462.8 up to UAH 1211.8); to improve quality of transportation process at the expense of decrease in maximum coefficient of bus capacity use to the limits of permissible value max_{=1.20; to provide}

non-exceedance of maximum admissible traffic interval of buses max

I =15 min. Final reserving of DATP

11255 PJSC vehicle fleet for the routes has been performed on the basis of the calculated coefficient

k

_i

References

1. Spirin, I.V. Transporting passengers by public transport: reference book. Мoscow: IKTs “Akademkniga”, 2004, 413 pp.

2. Taran, I.А.; Novitskii, А.V.; Litvin, V.V. Determining basic causes of high prime cost of passenger transportation on public bus routes of the city of Dnipropetrovsk. Proceedings of the 8th _{international scientific} and practical conference “Modern technologies and prospects if motor transport development”, Vinnytsia: VNTU, 2015, 235-238.

3. Kotsuk, О.Ya. Interaction between the transportation means: tutorial. Кyiv: UTU, 1999; 107. 4. Methodology guidelines on bus assignment on public bus routes. М.: Minavtotrans RSFSR, 1979; 29.

5. Yefimov, Ye.S.; Kobozev, V.М.; Yudin, V.А. Theory of municipal passenger transportation. Мoscow: Vesshaia shkola., 1980; 535.

6. Antoshvili, М.Ye.; Varelopulo, G.А.; Khrushchev, М.V. Organizing municipal bus transportation involving mathematical methods and ECM. Мoscow: Transport, 1974, 104.

7. Dolia, V.К. Passenger transportation: [text-book]. Kharkiv: Fort, 2011; 504.

8. Taran, I.; Litvin, V. Determination of rational parameters for urban bus route with combined operating mode. Transport Problems 2018, 13(4), 157-171.

9. Why has the fare risen: calculations, costs, tariffs [Internet source]. Available online: https://dengi.informator.ua/2018/03/22/pochemu-vyrosla-tsena-na-proezd-v-dnepre-raschety-traty-tarify. 10. Organizing and controlling passenger transportation. Ed. by V.S. Marunich, Prof. L.G. Shmorgun, Кyiv:

Milenium, 2017, 528.